Mylona.styliani 10900371 11MDE60ATH1 Yp Erg4

10900371_11MDE60ATH1_yp_erg4.doc

60

4 , 2011-2012 &

: - : :

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( ) (.. 06511) . - 11601 4 28 2012 28 2012

, , . , .

( - ) ( ) /

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4 , 2011-2012 ( ) 1 ( ) ( ) . , , , . , , , , . , , ( ) . 1 3 -1 5 -3 () 2 1 2 3 1 3 2 -1 1 1 4 1 -2 2 0

()

1 2 3 4

: ) , minimax , . (1 ). ) , . (1 ). ) , . (2 .

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1 ) . minimax, ( ) ( ) maximin ( ) ( ) ( ), minimax ( -). , , ( ) . , . ( )

maximi n 1

( )

1 2 3 4 minimax

1 3 -1 5 -3 5

2 1 2 3 1 3 2

3 2 -1 1 1 2

4 1 -2 2 0 2

1 -2 1 -3

V(A, Bi) V(B, Aj)

, maximin ( ) 1 ( 1-2 1-4 3-3) minimax ( ) 2 ( 1-3 3-4). , , . , .. 4


) , . . , . , 2 3 ( ). 4 1 3 ( ). , 1 2, 3 4 ( ). , 2 4 ( ). , 22, :: 1 3 2 1 1 2 3 4

) minimax () . V(A, Bi) i. , , V(A, B3)=V(A, B4) minimax ). : 2x1 + x3 = x1 + 2x3 x1 + x3 = 1. 1 3 x1 x3 3 Y3 2 1 4 Y4 1 2

: 2x1 + x3 = x1 + 2x3 2x1 x1 = 2x3 x3 x1 = x3 1 x3 = x3 1 = 2x3 x3 = = 0,5 x1 + x3 = 1 x1 = 1 x3 x3 = 1 0,5 = = 0,5 x1 = x3 = : V(A) = 2x1 + x3 = 2 * 0,5 + 0,5 = 1 + 0,5 = 1,50.. 5


V(B, A1) = V(B, A3) : 2y3 + y4 = y3 + 2y4 y3 + y4 = 1. : 2y3 + y4 = y3 + 2y4 2x3 x3 = 2y4 y4 y3 = y4 1 y4 = y4 1 = 2y4 y4 = = 0,5 y3 + y4 = 1 y3 = 1 y4 y3 = 1 0,5 = = 0,5 y3 = y4 = : V(B) = 2y3 + y4 = 2 * 0,5 + 0,5 = 1 + 0,5 = 1,50 , : : , 0, , 0 : 0, 0, , V: 1,5 ( ) , , 1 (0,5) 3 (0,5) 3 (0,5) 4 (0,5).

2 Net Electronics, Inc, modems, ISDN modems 64 128 . 20/modem 64 30/modem 128. , 100.000 modems 64 modems . , modems 128 90.000 . , Net Electronics, (64 128), 1.000 500 modems , 320. ) Net Electronics, Inc., . . (1 ) ) . ( ). (2 )

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2 ) Net Electronics, Inc modems, , , , . x1 ISDN modems 64 x2 ISDN modems 128. modem 64 20 modem 128 30 . , x1 modems 64 x2 modems 128 z = 20x1 + 30x2 . : 100000 modems 64 x1 100000. modems 128 90000 x2 90000. 320 , : 1000 modems 64, x1 modems 64 1 /1000 x1 , 500 modems 128, x2 modems 128 1 /500 x2 . 320 , : 1/1000x1 + 1/500x2 320.

: Max z = 20x1 + 30x2 : 1) x1 100000 2) x2 90000 3) 1/1000x1 + 1/500x2 320 ( x1, x2 0 ).

)

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, (100000, 0), (100000, 90000), (140000, 90000) (320000, 0) . , z = 6000000 z , . , z 6400000 . : A B x1 100000 100000 140000 320000 x2 0 90000 90000 0 z = 20x1 + 30x2 20*100000+30*0=2000000 20*100000+30*90000=4700000 20*140000+30*90000=5500000 20*320000+30*0=6400000

, x1 = 320000 modems 64 x2 = 0 modems 128 z* = 6400000 .

3

. : 250 () 100 (). . (S1), (S2) (S3). . 8


. : () () S1 S2 S3 250 100 25 100 100 75

A) . (1 ) ) - , (optimistic approach), (conservative approach), minimax regret. (1 ) ) : P(S1)=0,65, P(S2)=0,15 P(S3)=0,20. . (1 )

3 )

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. () . d1 d2 (d1= d2= ) s1, s2 s3 (s1= , s2= s3= ). Payoffs

s1 s2 s3 1 s1 d2 3 s2 25

250

d1

2

100

100

100 s3 75

) (optimistic approach) maximax. 10


( ). . : () () () () s1 s2 s3 250 100 25 100 100 75

s1 s2 s3 250 100 25 100 100 75 Maximum payoff

250 100 250

Maximum Decision ()

, maximax = 250. (conservative approach) maximin ( ). , . : () () () () s1 s2 s3 250 100 25 100 100 75

s1 s2 s3 250 100 25 100 100 75 Maximum payoff

25 75 75

Maximum Decision ()

, maximin = 75.

- minimax regret . . 11


, . : () () s1 s2 s3 250 100 25 100 100 75

() ()

S1 S2 (250-250)=0 (100-100)=0 (250-100)=150 (100-100)=0 () () 50 100

S3 (75-25)=50 (75-75)=0

, minimax = = 50.

) , , , . () () P(S2)=0,15 S2 100 100

(S1)=0,65 S1 250 100

P(S3)=0,20 S3 25 75

(EV) = + EV ( ) = 0,65*250+0,15*100+0,2*25=162,5+15+5=182,5 EV ( ) = 0,65*100+0,15*100+0,20*75=65+15+15=95

( ). d1( )=182,5

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0,65

s1

182,5

0,15

s20,20

s30,65

s1 s 2

95

0,15

0,20

s3

- 1. , . (2006) , , , , . 2. , . (2002) , , . 3. http://academics.epu.ntua.gr/LinkClick.aspx? fileticket=3hyU6U6eG80%3D&tabid=380&mid=838 4. http://academics.epu.ntua.gr/LinkClick.aspx? fileticket=TEutWP3krj0%3D&tabid=377&mid=833 5. http://www.math.ntua.gr/~coletsos/Documents/Summary_of_OR.pdf 6. http://www.math.upatras.gr/~tsantas/DownLoadFiles/MBA_DecisionAnalysisA.pdf

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Mylona.styliani 10900371 11MDE60ATH1 Yp Erg4

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